If the sum of first n terms of an AP is $\frac{1}{2}[3n^2+7n]$ then find nth term and hence, write its 20th term.

Given: $S_n=\frac{1}{2}[3n^2+7n]$

To do: Find nth term and hence, write its 20th term.

Solution:

Let us take sum upto 1 term

$S_1=\frac{1}{2}[3+7]=5$

Let us take sum upto two terms

$S_2=\frac{1}{2}[3\times4+7\times2]=\frac{26}{2}=13$

We know,

$S_1=a_1=5$

$S_2=a_1+a_2=13$

$S_2-S_1=a_1+a_2-a_1$

$13-5=a_2$

$a_2=8$

We know $d=a_2-a_1$

d=$8-5=3$

n^th term of AP =$a_n= a + (n-1)d$

$5+(n-1)3$

$an= 2+3n$

Therefore, 20th term is $a_{20}= 2+3(20)=62$

Hence 20th term of AP is 62

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Updated on: 10-Oct-2022

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